Answer
(i) and (ii)
Work Step by Step
(i)
Addition can be performed only if the matrices have the same dimension.
A has the same dimension as A (itself), so this is possible.
(ii)
The scalar product $cA$ is the $m\times n$ matrix that is obtained by multiplying each entry of $A$ by $c.$
2A is defined for any dimension of A.
(iii)
A matrix product AB exists only if $A$ is an $m\times n$ matrix and $B$ is an $n\times k$ matrix ,
(the number of columns in the first must equal the number of rows in the second matrix.
For AA to exist, A must have the same number of rows and columns.
So, no, AA is not defined for any dimension.
